Ascertainment
Bias in a determination of the Primary
Sex Ratio:
a classroom demonstration
The Primary Sex Ratio
is the ratio of males to females in a
population: it is expected to be 1:1. One possible way
to count this is to ask a group of people how many brothers
and sisters are in their families (including themselves). For
example, n = 57 women in Biol2250 were asked
to give the counts for their families, with the results as
reported above. The ratio of male : female is heavily
skewed towards women, almost 2:1 [to be precise,
1.88:1] instead of the expected 1:1.
Why? A census limited to women is guaranteed to include a
large number of women (n = 11 out of 57 respondents)
that are "only children" (no boys, one girl), and also
a number of women from larger all-girl families (a further 12
respondents). Such a census also excludes the reciprocal
family types, those with single or all-boy makeup. The result
is an ascertainment bias, a mismeasurement of a
phenomenon by an error in which the measurement is made.
A partial correction is to exclude all respondents with no
brothers [first four lines], which in these data would give a
male : female ratio of 50:56. A bias in the other
direction is expected from a census limited to men.
[Homework:
Suppose the classroom measurement of primary sex ratio were
done for all undergraduates in the Department of Biology,
irrespective of sex. Would you expect a 1:1 ratio? Why or why
not? Hint: suppose you did this at the Royal Military
College.]